My vet has told me that they do know when another kitty in the
household is ill. Usually they will not be kind to the sick kitty -
survival of the pack - they try to run off the sick one. Sometimes by
not letting the sick one have food, etc.

I had a very sensitive male cat and an ill female. Even though Dusty
was sensitive, he was very unkind to the female before her death from
cancer.